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JIGME NAMGYEL ENGINEERING COLLEGE

FLM201 FLUID MECHANICS

PRACTICAL LABORATORY MANUAL

Prepared by:

Dr. Bruce G. Wilson, P.Eng.

Department of Civil Engineering

University of New Brunswick

Fredericton, New Brunswick, Canada

November 2018


Experiment 1: FLOW MEASUREMENT

Aim: The objective of this experiment is to familiarize students with several typical methods of measuring the discharge in a pipe system during Steady Flow. The discharge determined using a Venturi meter, an orifice plate meter and a rotameter will be compared to the discharged measured using the Volumetric Flow Bench.

Apparatus:

1. TecQuipment Volumetric Hydraulics Bench

2. TecQuipment H10 Flow Measurement Apparatus (see Figure 1)

3. A stop watch

The main apparatus is shown in Figure 1. Water from the Hydraulic Bench enters the equipment through a Venturi meter, which consists of a gradually-converging section, followed by a throat and a long gradually diverging section. After a change in cross-section through a rapidly diverging diffuser, the flow continues along a settling length and through an orifice plate meter, manufactured from a plate with a hole of reduced diameter through which the fluid flows. Following a right-angled bend, the flow enters the rotameter. This consists of a transparent tube in which a float takes up an equilibrium position. The position of this float is a measure of the flow rate.

After the rotameter the water returns via a control valve to the Hydraulic Bench, where the flow rate can be measured directly by noting the time required for a given volume of water to be collected. The recommended method is to measure the time required to collect 10L of water. The equipment has nine pressure taps (A to I) as detailed in Figure 2, each of which is connected to its own manometer.


Figure 1 TecQuipment H10 Flow Measurement Apparatus

Figure 2 Flow Measurement Apparatus Detail


Procedure:

1. Place the flow measurement apparatus on the hydraulic bench top. 2. Connect the up-stream side of the unit to the bench supply valve. 3. Connect the down-stream end of apparatus to a plastic tube which is

directed into the hydraulic bench for measuring discharge from the apparatus.

4. Switch on the bench supply and allow water to flow. 5. Set the apparatus control valves to approximately one third of their fully

open positions. Before allowing water to flow through the apparatus check whether the air purge valve on the upper manifold is tightly closed.

6. Release the air purge valve sufficiently to allow water to reach approximately half way up the manometer scale and open control valve approximately one third their fully open positions.

7. When a steady flow is maintained, measure the flow rate with the Hydraulic Bench and the stopwatch. Record the values in Table 1.

8. Record the readings of each of the manometers in Table 2. 9. Record the level of the rotameter in Table 2. 10. Repeat steps 7, 8 & 9 for a wide range of different flow rates.

Observations:

Record your observations in Tables 1 and 2 below.

Calculations:

Using your recorded observations, perform the following calculations:

1. The discharge rate measured using the hydraulic bench can be determined using the

formula , where V is the volume and T is the time. Record your result in m3/s.

(Note that 1 L/s = 0.001 m3/s.) 2. The discharge rate measured using the Venturi meter can be determined using the

formula 9.62 10 where hA and hB are the manometer readings at A and B. Note that this equation requires that you convert hA and hB from mm to m. The result, Q, is in m3/s.

3. The discharge rate measured using the orifice meter can be determined using the

formula 8.46 10 where hE and hF are the manometer readings at E and F. Note that this equation requires that you convert hA and hB from mm to m. The result, Q, is in m3/s.

Report: Your Laboratory Report should include:

1. A Title Block with your name, the date, and the name of the experiment. 2. A short statement of the purpose of the laboratory - in your own words. 3. Data and Results Tables as presented below. 4. A graph plotting the discharge from (i) the Venturi Meter, (ii) the Orifice Meter, and

(iii) direct measurement on the y axis vs the Rotameter readings on the x axis. 5. A brief discussion of the results and potential sources of error. 6. A brief Conclusion


Table 1: Measured Discharge Rate

TEST NO.

Volume of Water, V(L)

Time, t(s)

Flow Rate, Q (m3/s)

1

2

3

4

5

Table 2: Manometer Tube Readings

TEST NO.

1 2 3 4 5

Man

ometer Level (mm)

A

B

C

D

E

F

G

H

I

Rotameter Reading

Table 3: Results

TEST NO.

Calculated

Discharge

(m3/s)

1 2 3 4 5

Venturi Meter

Orifice Meter

Hydraulic Bench


Experiment 2: Bernoulli Equation applied to a Venturi Meter

Purpose

The aim of this experiment is to measure fluid head at various points along a Venturi meter for various flow rates and to examine the validity of Bernoulli’s equation as a function of position along the meter.

Learning Objectives

The Bernoulli exercise involves measurements of static pressure head and examines the validity of Bernoulli’s Equation along a duct of variable cross section. After successfully completing the exercise students should be able to

Apply Bernoulli’s Equation along a pipe of varying cross section.

Identify any discrepancies within the experimental results and provide a plausible explanation for observed discrepancies.

Apparatus

Figure 1 is a schematic of the TecQuipment Venturi Meter apparatus. Water is pumped into the meter through a flexible hose. Inserted in the hose is a valve for controlling the flow rate. Water passes through the Venturi device and a secondary valve before discharging into the reservoir tank. A set of pressure taps along the Venturi wall provide the pressure distribution along the length of the convergent-divergent passage. Each tap is connected to a vertical manometer tube mounted in front of a scale for direct readings of pressure head difference in millimeters of water. The manometer tubes connect at their top ends to a common manifold that has a small air valve. The hand pump (attached to the side of the apparatus) can be used to adjust the air pressure in the manifold to adjust the uniformity of the water levels in the manometer at higher flow rates so that the water levels fit within the measuring scale of the manometers scales. The secondary valve adjusts the overall pressure in the system to control the location of the static pressure manometer interfaces.

Theory

The Venturi Effect is named after the Italian physicist Giovanni Venturi from the 18th century. He found that the pressure of a moving fluid drops when it passes through a constriction in a pipe. Around the same time, a Dutch-Swiss mathematician, Daniel Bernoulli, showed that the change in velocity of a fluid is directly related to the change in its pressure (potential energy) assuming that the flow is steady, incompressible, inviscid, without losses, and with no work.


Figure 2 shows an incompressible fluid flowing along a convergent-divergent pipe with three pressure taps. One tap measures the upstream pressure at section 1, the second measures the pressure at the throat (section 2) and the third measures pressure downstream at an arbitrary section 3. The cross-sectional area at the upstream section is a1, at the throat is a2, and at the arbitrary location is an. Piezometer tubes at these sections register h1, h2, and hn as shown.

Figure 1. Schematic of the Venturi meter apparatus. (taken from TecQuipment H5 user guide)

Figure 2. Idealized depiction of the relative magnitude of the velocity head and pressure head along a convergent-divergent pipe. (taken from TecQuipment H5 user guide)


[1]

Assuming Bernoulli’s Equation is valid and expressing the pressure in terms of the manometer readings yields

2 2 2

where v1, v2, and vn are the velocities through sections 1, 2, and n. The velocities at 1, 2, and n are further related through the continuity equation (conservation of mass) which states that the mass flow rate through each section is constant (no accumulation of mass) or

or

where is the mass flow rate, is the density, and is the volume flow rate. If the fluid is incompressible then

and if v1, v2, and vn represent the average velocity through each section then Eqn. 4 becomes

where A is the cross sectional area at a given point. Thus the velocity at each section may be determined from the measured flow rate knowing the cross sectional area at each point along the length of the Venturi meter.

Procedure

1) Record dimensions of the Venturi apparatus at all locations along the convergent-divergent section.

2) First close the valve attached to the pump then open the valve 1.5 to 2 full turns. 3) Open the secondary valve (valve downstream of the Venturi meter) completely. 4) Turn on the pump. It may take a few seconds to for the pump to prime and the water to

begin flowing through the Venturi meter. 5) As water begins to flow through the apparatus, water should rise up into the manometer

tubes. Make sure the fluid does not rise completely to the top of any tube. If it appears as though it will rise to the top, make sure the secondary valve is completely open then close the valve near the pump to reduce the flow rate.

6) Once steady state is reached you may notice air bubbles trapped in the manometers. These need to be removed. Tilt the entire Venturi meter and gently pluck each manometer to dislodge the bubbles. Repeat until all the bubbles have risen to the top.

7) Increase the flow rate until the far left manometer is near the top. You may notice that not all of the manometers are filled.

8) To fill all manometers slowly close the secondary valve until liquid is present in all tubes. Be careful that the fluid in the other manometers does not exceed the scale

[2]

[3]

[4]

[5]


maximum. If it appears as though it will, either decrease the flow rate or increase the back pressure with the hand pump provided (Note: it is unlikely you will need to do this).

9) The device should now be ready. Measure the manometer readings at each position for three different flow rates.

Data Analysis

For the measured flow rates, calculate the velocity at each point along the Venturi meter. With the velocities and manometers readings calculate the total fluid head along the length of the Venturi meter for each flow rate. Plot the pressure head, velocity head, and total head as a function of distance along the Venturi meter, x.

Are trends consistent with Bernoulli’s Equation observed?

Possible Discussion Points

If Bernoulli’s Equation is valid along the length of the Venturi meter then the total head at each point should be constant. If the total head is not constant, head loss (and therefore energy loss) is present in the system. It is possible that Bernoulli’s Equation is satisfied in sections of the Venturi meter but not necessarily across the entire meter. Is this observed?


Table 1: Measured Discharge Rate

TEST NO.

Volume of Water, V(L)

Time, t(s)

Q=V/T (m3/s)

1

2

3

Table 2: Peizometer Tube Readings

TEST NO.

1 2 3

Peizometer Level (mm)

A

B

C

D

E

F

G

H

J

K

L


Table 3: Results

Piezometer A B C D E F G H J K L

Distance x (mm) ‐13 7 19 33 48 63 78 93 108 123 143

Diameter (mm) 26.00 23.20 18.40 16.00 16.79 18.47 20.16 21.84 23.53 25.21 26.00

CrossSection Area, A (m2)

Discharge, Q

(m

3/s)

____________

Pressure Head,

P/g (m)

Flow Velocity v=Q/A (m/s)

Velocity Head (v2/2g)

Total Head

(P/g+ v2/2g) (m)

Discharge, Q

(m

3/s)

____________

Pressure Head,

P/g (m)



Total Head

(P/g+ v2/2g) (m)

Discharge, Q

(m

3/s)

____________

Pressure Head,

P/g (m)



Total Head

(P/g+ v2/2g) (m)


Experiment 3: Calculate the Discharge Coefficient for a Venturi Meter

Purpose

The aim of this experiment is to calculate the discharge coefficient for a Venturi meter. The discharge coefficient is a dimensionless number that accounts for head loss in the meter.

Learning Objectives

In Experiment 1 we used Venturi meter to measure the flow rate in a pipe system. For this lab, a discharge coefficient which related head loss in the Venturi to flow rate was provided. In Lab 2 we learned that there was a loss of energy in a Venturi meter. In this experiment, we will determine the discharge coefficient for the Venturi meter by measuring head loss at various flow rates.

Apparatus

This lab will also use the TecQuipment Venturi Meter apparatus shown in Figure 1. A description of the apparatus is given in the description of Experiment 2: Verifying the Bernoulli Equation.

Theory

The theoretical discharge equation for a Venturi meter (shown in Figure 2) is based on the energy equation with the assumption that there are no losses between the upstream end of the Venturi to the throat of the Venturi. In order to account for these losses in a real Venturi meter, a coefficient of the meter is used. The discharge equation for a horizontal Venturi is then:

2

1

where:

Q = discharge, m3/s

C = discharge coefficient of the Venturi meter, dimensionless

A1 = area at the upstream end of the Venturi, m2

A2 = area at the throat of the Venturi, m2

h1 = piezometric head at the upstream end of the Venturi, m

h2 = piezometric head at the throat of the Venturi, m

g = acceleration due to gravity

The value of C depends on the Reynolds number of the flow and the type of Venturi. For any given Venturi meter with specified dimensions, the following value will be a constant:


2

1

Therefore, we can write the discharge through a Venturi meter as:

or

Thus, a plot of vs Q should lie on a straight line.

Figure 1. Schematic of the Venturi meter apparatus. (taken from TecQuipment H5 user guide)


Procedure

1) Record dimensions of the Venturi apparatus at all locations along the convergent-divergent section.

2) First close the valve attached to the pump then open the valve 1.5 to 2 full turns. 3) Open the secondary valve (valve downstream of the Venturi meter) completely. 4) Turn on the pump. It may take a few seconds to for the pump to prime and the water to

begin flowing through the Venturi meter. 5) As water begins to flow through the apparatus, water should rise up into the manometer

tubes. Make sure the fluid does not rise completely to the top of any tube. If it appears as though it will rise to the top, make sure the secondary valve is completely open then close the valve near the pump to reduce the flow rate.

6) Once steady state is reached you may notice air bubbles trapped in the manometers. These need to be removed. Tilt the entire Venturi meter and gently pluck each manometer to dislodge the bubbles. Repeat until all the bubbles have risen to the top.

7) Increase the flow rate until the far left manometer is near the top. You may notice that not all of the manometers are filled.

8) To fill all manometers slowly close the secondary valve until liquid is present in all tubes. Be careful that the fluid in the other manometers does not exceed the scale maximum. If it appears as though it will, either decrease the flow rate or increase the back pressure with the hand pump provided (Note: it is unlikely you will need to do this).

9) The device should now be ready. Measure the manometer readings upstream of the Venturi and at the throat of the Venturi for multiple flow rates.

Figure 2. Idealized depiction of the relative magnitude of the velocity head and pressure head along a convergent-divergent pipe. (taken from TecQuipment H5 user guide)


Data Analysis

1. Calculate the constant:

2

1

2. For five different measured flow rates, calculate the square root of the difference in piezometric head:

3. Plot the square root of the difference in piezometric head vs the discharge. 4. Measure the slope of a line through the plotted points and compare the value to the

theoretical value of the discharge coefficient, C.


Table 1: Observations

Volume of Water Time Peizometer Level

TEST NO.

V (L)

t (s)

hA (mm)

hD (mm)

1

2

3

4

5

Table 2: Results

V T hA hD Q hA ‐hD C

Run No. L s mm mm m/s m m0.5 ‐

1

2

3

4

5


Experiment #4: FLOW OVER WEIRS Aim: To determine the discharge coefficient for a rectangular notch and a V-notch weir.

Apparatus:

1. Hydraulic bench 2. Rectangular and V-notch weirs 3. Stop watch 4. Volumetric tank 5. Point gauge

Theory:

Weirs are used to measure the flow rate in open channels. Under ideal conditions, there is a unique relationship between the discharge and the head (or upstream depth) on the weir. The relationship depends on the weir type and shape and on the velocity of the water in the channel as it approaches the weir. In this experiment we will investigate two types of commonly used weirs: a rectangular weir and a V-notch weir. Other types of weirs, such as broad crested weirs, are also used in practice. Triangular weirs are useful for measuring a relatively wide range of flows. The triangular weir ensures that the nappe is always aerated and provides a greater range in head than that for a rectangular weir for the same range of discharge. The basic equation for discharge over a triangular weir is:

815

2 tan2 2 2

where: Q = discharge, m3/s Cd = discharge coefficient (dimensionless) g = acceleration due to gravity

θ = central angle at vertex of triangle, degrees H = head on weir above lowest point of triangular weir crest

(measured at about 4H upstream of the weir crest) v0 = velocity of approach, m/s

The velocity of approach is obtained from the continuity equation as follows:

where: P = the distance from the channel floor to the weir crest, m b = the width of the channel upstream of the weir, m The parameters P, H, v0 and P are depicted in Figure 1. The solution of the above equation for discharge would involve a trial and error procedure because a value of Q must be assumed in order to compute v0, the velocity of approach. Then v0 must be known in order to compute the correct value of Q.


Figure 1. Basic parameters involved in using a weir for discharge measurement (from Hwang and Houghtalen, 1996).

The discharge coefficient, Cd, has been evaluated from tests carried out in various laboratories. A graphical presentation of the variation of the discharge coefficient for triangular weirs with central angles between 10o and 90 o is shown in Figure 2 for various heads, H. This figure illustrates that the discharge coefficients determined by different laboratories are not in perfect agreement. If the value of P/H is greater than about 1.5, the velocity of approach is quite small and may be neglected in most cases. If the velocity of approach is neglected the equation for discharge over a triangular weir reduces to:

815

2 tan2

The discharge coefficient is thus:

815 2 tan 2

For flow over a rectangular weir,

23

2

So

23 2 b

Procedure:

1. Take the point gauge reading with the tip of the gauge at the flume floor. Obtain the point gauge reading corresponding to the crest of the weir (the lowest point in the notch). The distance P is the difference between these two readings.

2. Adjust the discharge valve to obtain a steady flow at the minimum discharge rate for which the nappe remains unattached from the face of the weir.

3. After waiting until the water level has stabilized, determine the head on the weir with the aid of the point gauge.

4. Increase the flow rate and obtain measurements of head and discharge as outlined in steps 3 and 4. Repeat the procedure until at least 4 determinations of head and discharge are made. The measurements should be relatively evenly distributed between the highest flow and the lowest flow. The main criteria for the discharge measurement is that the measurement errors should be minimized.


Figure 2. Variation of the coefficient of discharge with head and central angle for triangular weirs (from Daugherty et al., 1985).

Report:

1. Determine the measured discharge for each run. 2. Using the weir discharge equation, compute the discharge over the weir assuming that

the velocity of approach is negligible. 3. Determine the value of the discharge coefficient, Cd, using information provided with

these laboratory notes. 4. For the V-Notch weirs, plot on one graph Q and H5/2. 5. For the rectangular weir, plot Q and H3/2.


Observations: Rectangular notch

SI no. Volume of water

Time Q

(m3/s)

Gauge reading(m)

Height

(m) Cd Q H3/2

Initial - - - - - - -

1

2

3

4

5

Observations: V Notches (45°& 60°)

SI no. Volume of water

Time Q

(m3/s)

Gauge reading(m)

Height

(m) Cd Q H5/2

Initial - - - - - - -

1

2

3

4

5


Experiment #5: HEAD LOSSES IN A PIPING SYSTEM

Aim: The objective of this experiment is to obtain the following relationships:

a) Head loss as a function of volume flow rate in a Straight Pipe; b) Friction Factor as a function of Reynolds Number in a Straight Pipe c) Loss coefficient vs flow rate for various valves, bends, and fittings.

Apparatus:

1. TecQuipment Volumetric Hydraulics Bench

2. TecQuipment H16 Pipe Flow Apparatus (see Figure 1.1)

3. A stop watch

The apparatus, shown diagrammatically in Figure 1.1, consists of two separate hydraulic circuits, one painted dark blue, one painted light blue, each one containing a number of pipe system components. Both circuits are supplied with water from the same hydraulic bench. The components in each of the circuits are as follows:


Manometer Tube Number

Unit

1 Proprietary Elbow Bend 2

3 Straight Pipe 4 5 Mitre bend 6 7 Expansion 8 9 Contraction 10 11 150mm bend 12 13 100mm bend 14 15 50mm bend 16 Dark Blue Circuit 1. Gate Valve 2. Standard Elbow 3. 90° Mitre Bend 4. Straight Pipe

Light Blue Circuit 5. Globe Valve 6. Sudden Expansion 7. Sudden Contraction 8. 150mm 90° Radius Bend 9. 100mm 90° Radius Bend 10. 50mm 90° Radius Bend

In all cases (except the gate and globe valves) the pressure change across each of the components is measured by a pair of pressurized Piezometer tubes. In the case of the valves pressure measurement is made by U-tubes.

Procedure

1. Fully open the water control valve on the hydraulic bench. 2. With the globe valve closed, fully open the gate valve to obtain maximum flow

through the Dark Blue circuit. Record the readings on the piezometer tubes and the U- tube.

3. Measure the flow rate by measuring the time required to collect 5 L of water in the volumetric tank.

4. Repeat the above procedure for a total of five different flow rates, obtained by closing the gate valve, equally spaced over the full flow range.

5. Close the gate valve, open the globe valve and repeat the above experimental procedure for the Light Blue circuit.

6. Plot graphs between head losses vs the discharge squared (Q2) or velocity head v2/2g.


Observation Table: Dark Blue Circuit

Sl.no

Flow rate Piezometer tube Readings

(mm of water) Globe Valve U-tube (mm of water)

Volume (L) Time (s) 1 2 3 4 5 6 G1 G2

1

2

3

4

5

Observation Table: Light Blue Circuit

Sl.no

Flow rate Piezometer tube (mm of water) Globe Valve U-

tube (mm of water)

Volume (L)

Time (s) 7 8 9 10 11 12 13 14 15 16 G1 G2

1

2

3

4

5


Calculations

Flow in a Straight Pipe

Purpose:

a) To measure the head loss in a straight pipe as a function of flow rate, Q. b) To measure the friction factor as a function of Reynolds number, Re.

1. Pipe diameter d = 0.0137 m 2. Pipe Length L = 0.914 m 3. Δ 4. Calculate the Flow Rate Q = Vol/Time 5. Calculate Velocity V = Q/A 6. Calculate the Reynolds Number

(Assume 9.4 10 m2/s)

7. Calculate friction factor Δ 2

8. Plot f vs Q2 9. Plot f vs Re

Sudden Expansion

Purpose: To compare theoretical and measured head increase at a sudden expansion as a function of flow rate, Q.

Given: d1 = 13.7mm

d2 = 26.4mm

According to Bernoulli, an expansion in a pipe should result in an increase in peizeometric head:

1

2

However, there is also a minor loss in energy at the expansion:

2

Therefore, the expected change in head at a sudden expansion is:


1

2 2

For each flow rate, calculate the following:

1. Calculate the flow rate, Q, and the velocities in the two pipe sections 2. Measure Δ 3. Calculate the expected head increase predicted by Bernoulli h1 – h2 4. Calculate the expected frictional head loss, hL 5. Plot head loss vs Q2 6. Compare the results

Sudden Contraction

Purpose: To compare theoretical and measured head loss at a sudden contraction as a function of flow

Given: d1 = 13.7mm

d2 = 26.4mm

According to Bernoulli, a sudden contraction in a pipe should result in a decrease in peizeometric head:

1

2

However, there is also a minor loss in energy at the expansion:

2

Therefore, the expected change in head at a sudden expansion is:

1

2 2

For this experiment, KL is estimated to be approximately 0.4.

For each flow rate, calculate the following:

1. Calculate the flow rate, Q, and the velocities in the two pipe sections 2. Measure Δ 3. Calculate the expected head increase predicted by Bernoulli h1 – h2 4. Calculate the expected frictional head loss, hL 5. Plot head loss vs Q2 6. Compare the results


Bends (150mm 90° Radius Bend , 100mm 90° Radius Bend, 50mm 90° Radius Bend)

Purpose: To measure K for three different bends as a function of flow rate, Q.

1. Measure head loss across each bend

Δ 2. Calculate K

Δ

2 Δ

3. Plot K vs Q for each Bend

Valves

Purpose: To measure K for a valve as a function of flow rate, Q.

1. Measure head difference in mm of water

Δ

2. Calculate K

Δ2

2 Δ

3. Plot K vs Q2

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